Séminaire du 28 avril 03, Markus Voege

Stars, watermelons and the $n$-friendly walker model

In the $n$-friendly walker model networks of lattice paths are considered. This model generalises the vicious walker model which Michael E. Fisher introduced by posing the following problem: ``Vicious drunks shoot on sight but they are short-sighted: thus on arriving at the same site they shoot each other dead.'' ``What is the probability that all walkers survive for $k$ steps?''

In this walk I will introduce the vicious walker and the $n$-friendly walker models and the configurations which are considered, watermelons and stars. I will then talk about techniques used to analyse some of the problems and I will present some results.